November 5-6, 2012
Shanghai, China
Session 5a: Some Research Results on Insurance
Risk Models with Dependent Classes of Business
1
Professor Kam C. Yuen Professor Kam C. Yuen The University of Hong Kong The University of Hong Kong
Introduction
2
Risk Management Regulatory Standard
•
Basel III
• Banking Industry
• Basel Committee on Banking Supervision
•
Solvency II
• “Basel for Insurers”
• Insurance Industry
• Insurance Industry
• European Commission
Risk Management
•
Enterprise Risk Management
•
Market Risk Management
•
Credit Risk Management
3
Risk Management
•
Insurance Risk Management
• Longevity Risk• Mortality Risk
• Adverse Selection, Moral Hazard, Information Asymmetry
• Catastrophic Riskp
• Asset and Liability Management
• Interest Rate Risk
Actuarial Quantities
•
Ruin Theory
• Surplus Process•
Dividend
• Optimal Strategies•
Risk Measures
Val e at Risk • Value-at-Risk•
Product Pricing
• Variable Annuity4
Why Dependence?
•
Systemic Risk
• Not systematic risk• Wikipedia:
• “It refers to the risks imposed by interlinkages and interdependencies in a system or market, where the failure of a single entity or cluster of entities can cause a cascading failure, which could potentially bankrupt or bring down the entire system or market.”
8
Dependence
•
Time Dependence
•
Class Dependence
9
Mathematical Tools
•
Multivariate Analysis
•
Copula
•
Common Shock
•
Thinning
•
Comonotonicity
•
Time Series
Risk Mitigant
•
Reinsurance
•
Derivatives
•
Catastrophe Bonds
10
Insurance Loss
•
Frequency Risk
•
Severity Risk
•
Modelling
Compound Poisson Risk Model
•
11
Ruin Probability
•
Outline
•
Thinning Model
•
Common Shock Model
•
Multivariate Time-series Risk Model
12
Thinning Model
•
Car Accidents
• Car Damage (Property Loss)
• Medical and Death Claims (Injuries, Life, Disabilities)
•
Fire
• House Damage
• House Damage
• Death and Medical Claims
Thinning Model
(Yuen and Wang, 2002)13
•
Thinning Model
(Yuen and Wang, 2002)Thinning Model
(Wu and Yuen, 2003)
14
•
Thinning Model
(Wu and Yuen, 2003)
•
15
Common Shock Risk Model
•
Natural Disaster
• Earthquake• Hurricane
• Flood
•
An event causes claims from
different
classes
classes
.
• That is why the term “common shock” is used.
Common Shock Model
(Yuen and Wang, 2002)16
•
Common Shock Model
(Yuen and Wang, 2002)•
17
Comparison of Ruin Probabilities
•
Comparison of Ruin Probabilities
18
Combining Thinning and Common Shock
(Wan, Yuen, Li, 2006)
•
•
Combining Thinning and Common Shock
19
•
Combining Thinning and Common Shock
(Wan, Yuen, Li, 2006)
Combining Thinning and Common Shock
20
Combining Thinning and Common Shock
(Wan, Yuen, Li, 2006)
Multivariate Time-series Risk Model
•
Capture
• Time dependence (Discrete time)
• Class dependence
•
Simple and straightforward
• Time-series modeling• AR MA ARMA
• AR, MA, ARMA
• Integer-valued time series
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Multivariate Time-series Risk Model
[Wan, Yuen, Li (2005), Zhang, Yuen, Li (2007), Wat (2012)]•
Multivariate Time-series Risk Model
[Wan, Yuen, Li (2005), Zhang, Yuen, Li (2007), Wat (2012)]22
•
Multivariate Time-series Risk Model
[Wan, Yuen, Li (2005), Zhang, Yuen, Li (2007), Wat (2012)]•
Upper Bound
for
Ruin Probability
Multivariate Time-series Risk Model
[Wan, Yuen, Li (2005), Zhang, Yuen, Li (2007), Wat (2012)]23
Multivariate Time-series Risk Model
(Wat, 2012)Multivariate Time-series Risk Model
(Wat, 2012)24
Multivariate Time-series Risk Model
(Wat, 2012)Multivariate Time-series Risk Model
(Wat, 2012)25
Multivariate Time-series Risk Model
(Wat, 2012)•
Multivariate Time-series Risk Model
(Wat, 2012)26
Premium Calculation
•
Ruin probability
• Measure riskiness• Estimate the capital level
• Calculate premium
Premium Calculation
(Yuen, Yang, Chu, 2001)•
27
•
Premium Calculation
(Yuen, Yang, Chu, 2001)•
The
premium
collected is
Premium Calculation
(Yuen, Yang, Chu, 2001)28
•
Premium Calculation
(Yuen, Yang, Chu, 2001)29
Premium Calculation
(Yuen, Yang, Chu, 2001)Summary
•
There are a lot of methods in handling
i
t
f d
d
various types of dependence.
•
Different mathematical techniques are
involved.
•
Practicality is another issue.
Anyway it is a good starting point to
•
Anyway, it is a good starting point to
capture the features of dependence
structures.
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Risk is Opportunity
•
SOA Motto
References
• Gerber, H. U. (1979). An Introduction to Mathematical Risk Theory S S
Mathematical Risk Theory.S.S.
Huebner Foundation, Wharton School, Philadelphia.
• Wan, L. M., Yuen, K. C., & Li, W. K. (2005). Ultimate ruin probability for a time-series risk model with dependent classes of insurance business. Journal of Actuarial Practice, 12, 193-214.
• Wan, L. M., Yuen, K. C., & Li, W. K. (2006). Analysis of an Insurance Risk Model with Thinning
Dependence and Common Shock. Journal of Actuarial Practice, 13, 147-164.
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References
• Wat, K. P. (2012). Discrete-time Insurance Risk Models with Dependence Structures.PhD Thesis. The University with Dependence Structures. PhD Thesis. The University of Hong Kong.
• Wu, X., & Yuen, K. C. (2003). A discrete-time risk model with interaction between classes of business.
Insurance: Mathematics and Economics, 33, 117-133.
Y K C G J & W X (2006) O h fi
• Yuen, K. C., Guo, J., & Wu, X. (2006). On the first time of ruin in the bivariate compound Poisson model. Insurance: Mathematics and Economics, 38, 298-308.
References
• Yuen, K. C., & Wang, G. (2002). Comparing two models with dependent classes of business ARCH
models with dependent classes of business. ARCH, Society of Actuaries, 22 pages.
• Yuen, K. C., Yang, H., & Chu K. L. (2001). Premium Calculation Using the Probability of Ruin . Journal of Actuarial Practice, 9, 247-262.
• Zhang, Z., Yuen, K. C., & Li, W. K. (2007). A time-g ( ) series risk model with constant interest for
dependent classes of business. Insurance: Mathematics and Economics, 41, 32-40.
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Professor Kam C. Yuen Professor Kam C. Yuen The University of Hong Kong The University of Hong Kong
